Place value and numbers
Each digit has a value that depends on its place. In 4,729 the digit 4 means 4,000 only because of where it sits.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 4 | 7 | 2 | 9 |
4,729 = 4,000 + 700 + 20 + 9. This is called expanded form.
Comparing numbers
Start from the left-most place. 4,729 > 4,692 because 7 hundreds is more than 6 hundreds.
Addition and subtraction
Adding
Line up the places and add from the ones. If a column reaches 10 or more, carry to the next place.
368 + 475 = 843
Subtracting
Subtract from the ones. If the top digit is too small, regroup from the next place.
602 − 278 = 324
Check your work: addition and subtraction undo each other. If 368 + 475 = 843, then 843 − 475 must equal 368.
Multiplication and division
Multiplication is repeated addition: 4 × 3 means four groups of three. Division shares a total into equal groups or finds how many groups fit.
Times table helper
Tricks
- ×2: double it.
- ×5: answers end in 0 or 5.
- ×9: the digits of the answer add up to 9 (9 × 4 = 36, and 3 + 6 = 9).
- ×10: add a zero.
Fractions
A fraction names equal parts of a whole. In 3/4, the bottom number (denominator) says how many equal parts, and the top number (numerator) says how many we have.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
Equivalent fractions
Multiply or divide the top and bottom by the same number. 1/2 = 2/4 = 4/8 = 50/100.
Adding fractions with the same denominator
Add the numerators and keep the denominator: 2/8 + 3/8 = 5/8.
Geometry and measurement
Perimeter
Distance around a shape. Rectangle: 2 × (length + width).
Area
Space inside a shape. Rectangle: length × width.
Volume
Space inside a solid. Box: length × width × height.
| Shape | Sides | Fact |
|---|---|---|
| Triangle | 3 | Angles add to 180° |
| Square | 4 | All sides equal, 4 right angles |
| Pentagon | 5 | Angles add to 540° |
| Hexagon | 6 | Honeycomb cells |
Word problems
- Read the whole problem and say it in your own words.
- Underline the question and circle the numbers.
- Choose an operation: total means add, left means subtract, groups mean multiply, sharing means divide.
- Solve, then check that your answer makes sense.
A class has 6 tables with 4 students each. 3 students are absent. How many students are present?
6 × 4 = 24, then 24 − 3 = 21.
Practice generator
Choose a type and answer as many as you like.